Dynamic voltage scaling scheduling  mechanism for sporadic, hard real-time tasks with resource sharing

ABSTRACT

A dynamic voltage scaling scheduling method executes one of the steps. When one task in the delayed task set requires for being executed, a working voltage required for executing the task is increased, and the task is removed from the delayed task set; when one task in the delayed task set requires for sharing resources, the working voltage required by the task is set as the current working voltage or a larger one in the minimum upper bounds of all the works requiring for sharing resources; and when one task does not belong to the delayed task set, but the waiting time has exceeded the period of the work, the working voltage for executing the task is reduced, and the task is added in the delayed task set.

This non-provisional application claims priority under 35 U.S.C. §119(a) on Patent Application No(s). 095147265 filed in Taiwan, R.O.C. onDec. 15, 2006, the entire contents of which are hereby incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention relates to a task scheduling method, and moreparticularly, to a dynamic voltage scaling scheduling method forsporadic and hard real-time tasks with resource sharing.

2. Related Art

An embedded system is a device for controlling, monitoring, or assistingthe operation of an apparatus, a machine, or even a factory, which is acombination tightly integrated with computer software and hardware. Innewly-emerged embedded system products, the most common ones includemobile phone, PDA, GPS, Set-Top-Box, embedded server, and thin client.

The embedded system has a lot of differences with the desktop computersystem, and the microprocessor of most embedded systems is developed inmanner of SoC. As for the flow of developing software, the software ofthe embedded system always exists in form of a firmware, therefore, thedevelopment in terms of software is also different from the developmentof desktop computer programs, and it is very common for the developmentof embedded system to develop software and hardware at the same time.

Most of the current embedded systems are developing towards the trend ofbeing mobile, networked, and automatic. Since the executed softwaremodules always have the real-time requirement and are limited by theelectric power, how to achieve the real-time task scheduling that meetsthe highest energy-saving requirement has always been an important keytechnique in the real-time operating system used in the current embeddedsystem.

In the currently existed techniques, multitasking scheduling is mostlyachieved with fixed voltage and time division, or the energy-savingobjective is achieved by way of static voltage scaling through usingmultilevel voltage scaling. The tasks are designated with differentpriority levels, the processing time is allocated according to thepriority levels, and thus the tasks with different priority levels canobtain different processor time and different executing order. On theother hand, the energy-saving objective is achieved by setting differentexecuting voltages according to different power supply states and taskrequirements. The current mechanism has an easy implementation manner,and does have the energy-saving effect, however, it can only be appliedin a common computer architecture with several and discrete voltagelevels, but cannot guarantee to meet the hard real-time requirement,thus it has a very limited performance in terms of energy-saving. Inaddition, when there are sporadic and resource-sharing tasks, it is hardto meet the hard real-time requirement.

Moreover, when considering the scheduling of a task set, the dependencebetween different tasks must be taken into consideration, for example,the accessing of the software resources for different tasks, so as toavoid excessive context switch, which consumes excessive electricalpower.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to provide a dynamicvoltage scaling scheduling method, which calculates a feasible minimumvoltage according to the deadline required by the task and softwareresource utilization, so as to dynamically adjust the scheduling.

The dynamic voltage scaling scheduling method according to an embodimentof the present invention is used for scheduling tasks in a delayed taskset, wherein a property of a task is determined first, and when the taskbelongs to the delayed task set or the task does not belong to the taskcollection but the waiting time has exceeded a period of the task, oneof the following steps is executed. When one task in the delayed taskset requires for being executed, a working voltage required forexecuting the task is increased, the task is removed from the delayedtask set, and the method returns to the step of determining the propertyof the task. When one task in the delayed task set requires for sharingresources, the working voltage required by the task is set as a currentworking voltage or a larger one in least upper bounds of all the tasksrequiring for sharing resources, and the method returns to the step ofdetermining the property of the task. When one task not belonging to thedelayed task set exists, and the waiting time of the task has exceededthe period of the task, the working voltage required for executing thetask is reduced, the task is added in the delayed task set, and themethod returns to the step of determining the property of the task.

The dynamic voltage scaling scheduling method according to the presentinvention meets the requirements of hard real-time. Thus, it will serveas a software component to be responsible for the scheduling of hardreal-time tasks including periodic, non-periodic, and sporadic tasks,and further improves energy efficiency, such that it is more applicableto an embedded system.

The dynamic voltage scaling scheduling method according to the presentinvention comprises periodically calculating an optimum start/end timeand a minimum executing voltage of the scheduling of the tasks inreal-time according to the property of the task to be executed, therebyachieving the real-time and energy saving requirements. The factor ofsoftware-resources sharing is also taken into consideration during thescheduling, such that the scheduling of the task has more flexibility.

The above description relevant to the content of the present inventionand the following description of the embodiments are used to exemplifyand explain the spirit and principle of the present invention, andprovide a further explanation of the claims of the present invention.

Further scope of applicability of the present invention will becomeapparent from the detailed description given hereinafter. However, itshould be understood that the detailed description and specificexamples, while indicating preferred embodiments of the invention, aregiven by way of illustration only, since various changes andmodifications within the spirit and scope of the invention will becomeapparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given herein below for illustration only, whichthus is not limitative of the present invention, and wherein:

FIG. 1 is a schematic view of a scheduling process for the dynamicvoltage scaling scheduling method according to the present invention;

FIG. 2 is a block diagram of the dynamic voltage scaling schedulingsystem according to the present invention;

FIG. 3 is a flow chart of the dynamic voltage scheduling methodaccording to the present invention;

FIG. 4 is a flow chart of voltage scaling in the dynamic voltagescheduling method according to the present invention.

FIG. 5 shows the scheduling process according to the prior art; and

FIG. 6 shows the dynamic voltage scheduling process according to thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

The detailed features and advantages of the present invention aredescribed in detail in the following embodiments, which is sufficientfor any skilled in the art to understand the technical content of thepresent invention and implement accordingly. Any skilled in the art caneasily understand the objectives and advantages of the present inventionfrom the content disclosed in the detailed description, claims, anddrawings.

Referring to FIG. 1, it is a schematic view of a scheduling architectureapplicable for the dynamic voltage scaling scheduling method accordingto the present invention.

Generally, tasks may be classified into four types, namely, hardreal-time tasks, soft real-time tasks, non real-time tasks, and monitorservice tasks. During the scheduling process, the tasks are categorizedinto four task collections, i.e., a hard real-time task collection 10, asoft real-time task collection 20, a non real-time task collection 30,and a monitor service task collection 40. The hard real-time taskcollection 10 is divided into periodic tasks 11 and sporadic tasks 12according to the occurring time. Each type of tasks has an exclusivequeue 13, 14, 21, 31, 41 for the tasks to wait. The service time of eachtask is ensured by a constant bandwidth service (CBS) 15, 16, 17, 22,32, 42. All the CBSs are served by an Early Deadline First (EDF)scheduler 50, and the bandwidth (calculation capability) of a centralprocessing unit (CPU) 60 is distributed to all the CBSs 15, 16, 17, 22,32, 42.

In the present invention, the feasible minimum voltage of each task iscalculated according to the deadline required by the task and thesoftware resource utilization. The executing process mainly includeschecking a scheduling feasibility and calculating a scheduling voltage.Referring to FIG. 3, it is a flow chart of a dynamic voltage schedulingmethod according to the present invention.

The method of FIG. 3 is executed by the CPU 60 of FIG. 1. As shown inFIG. 2, a determining module 61 and an adjusting module 62 are providedin the CPU 60 by way of software or hardware. The determining module 61determines a property of a task according to task information offered bysystem software. The adjusting module 62 adjusts a working voltagerequired for executing the task either when the task belongs to thedelayed task set or when the task does not belong to the task collectionbut a waiting time has exceeded a period of the task. When one task inthe delayed task set requires for being executed, the adjusting module62 increases a working voltage required for executing the task, removingthe task from the delayed task set. When one task in the delayed taskset requires for sharing resources, the adjusting module 62 sets theworking voltage required by the task as a current working voltage or asa larger one in least upper bounds of all tasks requiring for sharingresources. When one task not belonging to the delayed task set exists,and the waiting time of the task has exceeded the period of the task,the adjusting module 62 reduces the working voltage required forexecuting the task, adding the task in the delayed task set.

First, the scheduling feasibility is checked (Step 70), and if thefeasibility of scheduling is confirmed, the scheduling voltage of eachtask is determined according to whether the task requires for sharingresources (Step 71).

Considering that the task collection in the system is T={T₁, T₂, . . . ,T_(n)}, and the period of the task T_(i) is an increasing subsequence{P_(i)}, that is, if i>j, P_(i)≧P_(j), wherein P_(i) is the period ofT_(i). In addition, the task collection T shares m different softwareresources, R={R1, R2, . . . , Rn}. The executing time required by T_(i)is e_(i). The check of the scheduling feasibility is to check the systemutilization and to ensure that the tasks sharing the resources havefeasible scheduling conditions.

The system utilization calculates whether the utilization for finishingall the tasks will not exceed 1, i.e.,

${{\sum\limits_{i = 1}^{n}\frac{e_{i}}{P_{i}}} \leq 1},$

so as to ensure that the CPU is not overloaded.

The check of the feasibility for tasks sharing the resources is achievedthrough Equation

${{\frac{e_{i} + {\sum\limits_{j = 1}^{i - 1}{\left\lfloor \frac{L}{P_{i}} \right\rfloor e_{j}}}}{L} + {\sum\limits_{j = {i + 1}}^{n}\frac{e_{j}}{p_{j}}}} < 1},{{for}\mspace{14mu} {\forall i}},{1 < i \leq {{n\hat{}{\left( {r_{i} \neq 0} \right)\hat{}\left( {T_{i} \neq {TD}} \right)}}{\forall{{L \cdot P_{ri}} < P_{i}}}}},$

so as to ensure that the tasks sharing the resources have the feasiblescheduling.

After finishing checking the scheduling feasibility, if the schedulingfeasibility comes to be true, the scheduling voltage of each task isdetermined according to the following events, with reference to FIG. 3.

When determining the scheduling voltage of each task, initial conditionsare set first (Step 80), wherein the working voltage is set as a standbyvoltage of the system, and all the tasks T={T₁, T₂, . . . , T_(n)} areset as the delayed task set TD.

Next, it is determined whether one task is an event that belongs to thedelayed task set and requires for being executed, or an event thatbelongs to the delayed task set and requires for sharing the resources,or an event that does not belong to the task collection but a waitingtime has exceeded a period of the task (Step 81).

Then, if the task T_(i) of the delayed task set TD requires for beingexecuted (Step 82), the working voltage of the task T_(i) is increased,and the task T_(i) is removed from the delayed task set TD (Step 83),and it returns to Step 81. The scaling volume of the working voltage is

${\alpha_{DVSST} = {\alpha_{DVSST} + \frac{e_{i}}{P_{i}}}},$

wherein α_(DVSST) indicates the current working voltage, e_(i) indicatesthe time required for executing the task, and P_(i) indicates the periodof the task.

If the task T_(i) of the delayed task set TD requires for sharing theresources (Step 84), the working voltage is set as the current workingvoltage or a larger one of least upper bounds of the tasks requiring forsharing the resources (Step 85), and it returns to Step 81.

The least upper bounds of all the tasks requiring for sharing theresources are determined through the following steps. If the last taskrequiring for sharing the resources is T_(i), the working voltagesrequired by the tasks with a period less than the period of T_(i) arecalculated through Equation

${{\alpha_{ST}\left( {i,L} \right)} = \frac{e_{i} + {\sum\limits_{j = 1}^{i - 1}{\left\lfloor \frac{L - 1}{p_{j}} \right\rfloor e_{j}}}}{L}},{P_{r_{i}} < L < {p_{i}.}}$

After all the possible working voltages are calculated, a minimumworking voltage is derived as

${{H_{ST}(i)} = {\underset{P_{ri} < L < p_{i}}{Min}\left( {\alpha_{ST}\left( {i,L} \right)} \right)}},$

then, the least upper bounds are obtained from,α_(lub)(i)=H_(ST)(i)+α_(LT)(i), and finally the largest one in the leastupper bounds is found out

$H_{lub} = {{\underset{\begin{matrix}{1 \leq i \leq n} \\{{r_{i} \neq {0\hat{}{Ti}}} \notin {TD}}\end{matrix}}{Max}\left( {\alpha_{lub}(i)} \right)}.}$

If the task is scheduled in the delayed task set TD, after Step 82 andStep 84, the working voltage is determined, and the task is sent to theEDF 50 for being executed. If the task waiting for being executed doesnot belong to the delayed task set TD but belong to an non-periodictask, and the waiting time has exceeded the period of the task (Step86), the working voltage of the non-periodic task is reduced, and thenon-periodic task is added in the delayed task set TD (Step 87), and itreturns to Step 81. The scaling volume of the working voltage

${\alpha_{DVSST} = {\alpha_{DVSST} - \frac{e_{i}}{P_{i}}}},$

wherein α_(DVSST) indicates the current working voltage, e_(i) indicatesthe time required for executing the task, and P_(i) indicates the periodof the task.

After the determination process through Steps 82, 84, and 86, if thereis no task to be executed, the scheduling voltage is scaled back to thestandby voltage and all the tasks are listed in the delayed task set TD(Step 88), and the method returns to Step 81.

The dynamic voltage scaling scheduling method disclosed in the presentinvention not only can be applied in the scheduling architecture in FIG.1, but also be applied in a recording medium, and when the recordingmedium is executed by a computer system, the steps described above areexecuted.

The above mentioned flow is illustrated below through an embodiment.

As for a task collection τ={T₁, T₂, T₃, T₄}, all the tasks in thecollection are ordered according to the increasing of the period, thatis, as for any two tasks T_(i) and T_(j), if i≧j, p_(i)≧p_(j). The taskcollection can share a unit resource collection R={R₁} with a reusablesequence. A parameter of this task is T_(i)=((e_(i), r_(i)), p_(i)),wherein e_(i) indicates the executing time of the task T_(i) under theworst condition, r_(i) indicates the resource requirement, and p_(i)indicates the period.

In this embodiment, the information of the used tasks in the taskcollection is described as follows.

T_(l)=((1,1), 4), T₂=((3,0), 10), T₃=((3,1), 20), T₄=((2,0), 30), and itis assumed that Task T₁ is released at Time 1, Task T₂ is released atTime 1, Task T₃ is released at Time 0, and Task T₄ is released at Time1.

Assuming that the unit of time is 1 ms, and the current time is 5.Before scheduling the task collection, the feasible conditions of thescheduling is first confirmed, and the system utilization is calculated.According to the above conditions, the system utilization is ¼+ 3/10+3/20+ 2/30=0.767. Therefore, the system utilization is less than 1, andthus satisfying the scheduling feasibility requirement.

In this embodiment, r₁=1, r₃=1, and thus Task T₁ and Task T₃ share thesame resource.

In this embodiment, when r₁=1, r₃=1, that is, Task T₁ and Task T₃ sharethe same resource, the values of all α_(ST) (3,L) in the interval [P₁+1,p₃] are calculated. Since the minimum period P₁ is equal to 4, theinterval [P₁+1,p₃] is equal to the interval [5,20]. The Equation ofα_(ST)(3,L) is shown as follows.

${{\alpha_{ST}\left( {3\text{,}L} \right)} = \frac{3 + \left\lfloor \frac{L - 1}{4} \right\rfloor + \left\lfloor \frac{L - 1}{10} \right\rfloor}{L}},{{{for}\mspace{14mu} 5} < L < 20.}$

Assuming that the current time is 5 ms, the value of α_(ST)(3,5) is:

${\alpha_{ST}\left( {3\text{,}5} \right)} = {\frac{3 + \left\lfloor \frac{5 - 1}{4} \right\rfloor + \left\lfloor \frac{5 - 1}{10} \right\rfloor}{5} = {0.8.}}$

The maximum value of α_(ST)(3,L) in the time interval [5, 20] isH_(st)(3). The value obtained by adding H_(st)(3) with α_(st)(3,L) isthe least upper bound of T₃, also known as α_(lub)(3).

${Then},{H_{lub} = {{\underset{{l \leq i \leq {4\mspace{14mu} r_{i}} \neq {0\hat{}T_{1}}} \notin {TD}}{Max}\left( {\alpha_{lub}(i)} \right)} = {{\alpha_{lub}(3)} = {0.733.}}}}$

Therefore, under the condition that the system utilization is ¼+ 3/10+3/20+ 2/30=0.767, as the scaled working voltage must meet the real-timeand resource sharing requirements, the value of the scaled workingvoltage must be the larger value of the least upper bound H_(lub) andthe current working voltage. Therefore, the following result isobtained,

α_(DVSSR)=Max(α_(DVSST) ,H _(lub))=Max(0.767,0.773)=0.773.

In order to verify the above method, referring to FIG. 5 and FIG. 6,FIG. 5 is a result of the prior art of dynamic voltage schedulingwithout considering resource-sharing, and FIG. 6 is a result obtainedfrom the present invention considering resource-sharing. Now, the taskcollections: T₁=((1,1),4), T₂=((1,0),5), T₃=((3,1),10) are taken intoconsideration.

After calculation, the system utilization before voltage scaling isU=0.75, which meets the requirement of scheduling feasibility, and thescheduling can be finished. J_(i,j) represents j^(th) release of Task i,the transverse axis represents the time, and the vertical axisrepresents the frequency (voltage) for executing the task. The areasunder the lines represent the consumed energy. Therefore, the energysaving performances of different scheduling methods can be seen from thefigure.

The method disclosed according to the present invention calculates theoptimum start/end time and the minimum executing voltage of a task to beexecuted according to the properties of the task, including real-timeproperty and periodic property, so as to achieve the requirements ofreal-time and energy saving. Moreover, the method disclosed in thepresent invention also takes the resource sharing factor intoconsideration during scheduling, such that the scheduling of tasks hasmore flexibility, and the real-time requirement for periodic andsporadic tasks is ensured, thereby significantly improving the energysaving performance of the current mechanism.

The invention being thus described, it will be obvious that the same maybe varied in many ways. Such variations are not to be regarded as adeparture from the spirit and scope of the invention, and all suchmodifications as would be obvious to one skilled in the art are intendedto be included within the scope of the following claims.

1. A dynamic voltage scaling scheduling method for resource-sharing andhard real-time tasks, applicable for scheduling tasks in a delayed taskset, comprising: determining a property of a task, and executing one ofthe following steps, when the task belongs to the delayed task set orthe task does not belong to the task collection but a waiting time hasexceeded a period of the task; when one task in the delayed task setrequires for being executed, increasing a working voltage required forexecuting the task, removing the task from the delayed task set, andreturning to the step of determining the property of the task; when onetask in the delayed task set requires for sharing resources, setting theworking voltage required by the task as a current working voltage or asa larger one in least upper bounds of all tasks requiring for sharingresources, and returning to the step of determining the property of thetask; and when one task not belonging to the delayed task set exists,and the waiting time of the task has exceeded the period of the task,reducing the working voltage required for executing the task, adding thetask in the delayed task set, and returning to the step of determiningthe property of the task.
 2. The dynamic voltage scaling schedulingmethod as claimed in claim 1, wherein the method is executed under acircumstance that a system utilization does not exceed 1, and the systemutilization is ${{\sum\limits_{i = 1}^{n}\frac{e_{i}}{P_{i}}} \leq 1},$wherein e₁ indicates the time required for executing the task, and Piindicates the period of the task.
 3. The dynamic voltage scalingscheduling method as claimed in claim 1, wherein before the step ofdetermining the property of the task, the method further comprises astep of setting the working voltage as a standby voltage of the system,and setting all the tasks as the delayed task set.
 4. The dynamicvoltage scaling scheduling method as claimed in claim 1, wherein afterthe step of reducing the working voltage required for executing thetask, if no task is to be executed, the current working voltage isscaled to a standby voltage and all the tasks are set as the delayedtask set, and the method returns to the step of determining the propertyof the task.
 5. The dynamic voltage scaling scheduling method as claimedin claim 1, wherein in the step of increasing the working voltagerequired for executing the task, the increased voltage is${\alpha_{DVSST} + \frac{e_{i}}{P_{i}}},$ wherein α_(DVSST) indicatesthe current working voltage, e indicates the time required for executingtask i, and Pi indicates the period of task i.
 6. The dynamic voltagescaling scheduling method as claimed in claim 1, wherein in the step ofreducing the working voltage required for executing the task, thereduced voltage is${\alpha_{DVSST} = {\alpha_{DVSST} - \frac{e_{i}}{P_{i}}}},$ whereinα_(DVSST) indicates the current working voltage, e_(i) indicates thetime required for executing task i, and Pi indicates the period of taski.
 7. A recording medium, applicable being executed to schedule tasks ina delayed task set, comprising: determining a property of a task, andexecuting one of the following steps, when the task belongs to thedelayed task set or the task does not belong to the task collection buta waiting time has exceeded a period of the task, when one task in thedelayed task set requires for being executed, increasing a workingvoltage required for executing the task, removing the task from thedelayed task set, and returning to the step of determining the propertyof the task; when one task in the delayed task set requires for sharingresources, setting the working voltage required by the task as a currentworking voltage or as a larger one in minimum upper bounds of all thetasks requiring for sharing resources, and returning to the step ofdetermining the property of the task; and when one task not belonging tothe delayed task set exists, and the waiting time of the task hasexceeded the period of the task, reducing the working voltage requiredfor executing the task, adding the task in the delayed task set, andreturning to the step of determining the property of the task.
 8. Therecording medium as claimed in claim 7, wherein the method is executedunder a circumstance that a system utilization does not exceed 1, andthe system utilization is${{\sum\limits_{i = 1}^{n}\frac{e_{i}}{P_{i}}} \leq 1},$ wherein e_(i)indicates the time required for executing task i, and Pi indicates theperiod of task i.
 9. The recording medium as claimed in claim 7, whereinbefore the step of determining the property of the task, the methodfurther comprises a step of setting the working voltage as a standbyvoltage of the system, and setting all the tasks as the delayed taskset.
 10. The recording medium as claimed in claim 7, wherein after thestep of reducing the working voltage required for executing the task, ifno task is to be executed, the current working voltage is scaled to astandby voltage and all the tasks are set as the delayed task set, andthe method returns to the step of determining the property of the task.11. The recording medium as claimed in claim 7, wherein in the step ofincreasing the working voltage required for executing the task, theincreased voltage is ${\alpha_{DVSST} + \frac{e_{i}}{P_{i}}},$ whereinα_(DVSST) indicates the current working voltage, e_(i) indicates thetime required for executing the task, and Pi indicates the period of thetask.
 12. The recording medium as claimed in claim 7, wherein in thestep of reducing the working voltage required for executing the task,the reduced voltage is${\alpha_{DVSST} = {\alpha_{DVSST} - \frac{e_{i}}{P_{i}}}},$ whereinα_(DVSST) indicates the current working voltage, e_(i) indicates thetime required for executing the task, and P_(i) indicates the period ofthe task.
 13. A dynamic voltage scaling scheduling system, forscheduling tasks in a delayed task set, comprises: the adjusting of aworking voltage required for executing the task when the task belongs tothe delayed task set or the task does not belong to the task collectionbut a waiting time has exceeded a period of the task; wherein when onetask in the delayed task set requires for being executed, increasing aworking voltage required for executing the task, removing the task fromthe delayed task set; wherein when one task in the delayed task setrequires for sharing resources, setting the working voltage required bythe task as a current working voltage or as a larger one in least upperbounds of all tasks requiring for sharing resources; and wherein whenone task not belonging to the delayed task set exists, and the waitingtime of the task has exceeded the period of the task, reducing theworking voltage required for executing the task, adding the task in thedelayed task set.
 14. The dynamic voltage scaling scheduling method asclaimed in claim 1, wherein the scheduling is executed under acircumstance that a system utilization does not exceed 1, and the systemutilization is ${{\sum\limits_{i = 1}^{n}\frac{e_{i}}{P_{i}}} \leq 1},$wherein e_(i) indicates the time required for executing the task, and Piindicates the period of the task.
 15. The dynamic voltage scalingscheduling method as claimed in claim 1, wherein before determining theproperty of the task, the means for determining further setting theworking voltage as a standby voltage of the system, and setting all thetasks as the delayed task set.
 16. The dynamic voltage scalingscheduling method as claimed in claim 1, wherein if no task is to beexecuted, the means for adjusting adjusts the current working voltage toa standby voltage and sets all the tasks are as the delayed task set.17. The dynamic voltage scaling scheduling method as claimed in claim 1,wherein the increased voltage is${\alpha_{DVSST} + \frac{e_{i}}{P_{i}}},$ wherein α_(DVSST) indicatesthe current working voltage, e_(i) indicates the time required forexecuting the task, and Pi indicates the period of the task.
 18. Thedynamic voltage scaling scheduling method as claimed in claim 1, whereinthe reduced voltage is${\alpha_{DVSST} = {\alpha_{DVSST} - \frac{e_{i}}{P_{i}}}},$ whereinα_(DVSST) indicates the current working voltage, e_(i) indicates thetime required for executing task i, and Pi indicates the period of taski.